# Research Opportunities

## Postdoctoral Researchers

I do not have vacancies for postdoctoral researchers at present but they will appear here when available.

## Postdoctoral Fellowships

I very much encourage young researchers to apply for postdoctoral fellowships. I am happy to support and assist strong candidates that would like to apply for fellowships with MSSL as the host institution.

If you are interested in discussing this further then please email me, including '[Fellowship enquiry]' in the subject of your email. I receive many enquires and so will only reply if your expertise are well matched to my research interests and there is a high chance of submitting a successful application.

More information on various fellowships can he found here:

- Royal Society (RS) University Research Fellowship (URF)
- Royal Society (RS) Newton International Fellowships (for researchers coming from abroad)
- Royal Society (RS) Dorothy Hodgkin Fellowships
- STFC Ernest Rutherford Fellowships (ERF)
- Royal Astronomical Society (RAS) Fellowships
- Leverhulme Trust Early Career Fellowships (ECF)
- Royal Commission for the Exhibition of 1851 Fellowships
- Marie Curie Fellowships (for researchers coming from Europe)
- Daphne Jackson Fellowships (for researchers returning from a career break)

## PhD Students

The PhD projects that I offer are typically multi-disciplinary and include a combination of cosmology, statistics, and informatics (e.g. machine learning, signal processing, harmonic analysis, etc.). A relatively strong mathematical background is usually required for these types of projects. Strong programming skills are also an advantage.

If you are interested in discussing PhD projects further then please email me, including '[PhD enquiry]' in the subject of your email, and attach a CV. I receive many enquires and so will only reply if your expertise are well matched to my research interests and there is a high chance of submitting a successful application.

Further information on how to submit an official application to MSSL can be found here.

Further information on how to submit an official application via the UCL CDT in Data Intensive Science can be found here.

Brief overviews of current projects on offer are given below

### PhD project: Probabilistic deep learning for cosmology and beyond

The current evolution of our Universe is dominated by the influence of dark energy and dark matter, which constitute 95% of its content. However, an understanding of the fundamental physics underlying the dark Universe remains critically lacking. Forthcoming experiments have the potential to revolutionalise our understanding of the dark Universe. Both the ESA Euclid satellite and the Rubin Observatory Legacy Survey of Space and Time (LSST) will come online imminently, with Euclid scheduled for launch in 2023 and the Rubin LSST Observatory having recently achieved first light. Furthermore, the Simons Observatory is in advanced stages of construction. Sensitive statistical and deep learning techniques are required to extract cosmological information from weak observational signatures of dark energy and dark matter.

The classical approach of deep learning is to make single predictions. A single estimate of a quantity of interest, such as an image, is typically made. For robust scientific studies, however, single estimates are not sufficient and a principled statistical assessment is critical in order to quantify uncertainties. Bayesian inference provides a principled statistical framework in which to perform scientific analyses. In cosmology, in particular, Bayesian inference is the bedrock of most cosmological analyses. While such approaches provide a complete statistical interpretation of observations, which is critical for robust and principled scientific studies, they are typically computationally slow, in many cases prohibitively so. Furthermore, in such analyses prior information typically cannot be injected by a deep data-driven approach.

In the proposed project we will develop probabilistic deep learning approaches, where probabilistic components are incorporated as integral components of deep learning models. Similarly, we will also develop statistical analysis techniques for which deep learning components are incorporated as integral components. This deep hybrid approach, where statistical and deep learning components are tightly coupled in integrated approaches, rather than considered as add-ons, will allow us to realise the complementary strengths of these different approaches simultaneously. For some examples of related research, please see the following recent papers: McEwen et al. 2021; Spurio Mancini et al. 2022; Polanska et al. 2023 (although in this PhD project we will go beyond the Bayesian model comparison focus of these works).

Specifically, in this project we will develop novel probabilistic deep learning models, variational inference techniques and simulation-based inference approaches. These new methodologies will be applied to various cosmological problems and probes, focusing on the cosmic microwave background and weak gravitational lensing, and will include generative models for emulation and inference approaches for the estimation of not only the parameters of cosmological models but also to assess the most effective models and physical theories for describing our Universe.

The student should have a strong mathematical background and be proficient in coding, particularly in Python. The student will gain extensive expertise during the project in deep learning, going far beyond the straightforward application of existing deep learning techniques, instead focusing on the construction on novel probabilistic deep learning approaches and their application to novel problems in cosmology and beyond. The expertise gained in foundational deep learning will prepare the student well for a future career either in academia or industry. In particular, the emerging field of probabilistic deep learning is a speciality highly sought after in industry by many companies, such as Google/DeepMind, Facebook, Amazon and many others.

### PhD project: Geometric generative AI for cosmology and beyond

The current evolution of our Universe is dominated by the influence of dark energy and dark matter, which constitute 95% of its content. However, an understanding of the fundamental physics underlying the dark Universe remains critically lacking. Forthcoming experiments have the potential to revolutionalise our understanding of the dark Universe. Both the ESA Euclid satellite and the Rubin Observatory Legacy Survey of Space and Time (LSST) will come online imminently, with Euclid scheduled for launch in 2023 and the Rubin LSST Observatory having recently achieved first light. Furthermore, the Simons Observatory is in advanced stages of construction. Sensitive statistical and deep learning techniques are required to extract cosmological information from weak observational signatures of dark energy and dark matter.

Deep learning has been remarkably successful in the interpretation of standard (Euclidean) data, such as 1D time series data, 2D image data, and 3D video or volumetric data, now exceeding human accuracy in many cases. However, standard deep learning techniques fail catastrophically when applied to data defined on other domains, such as data defined over networks, 3D objects, or other manifolds such as the sphere. This has given rise to the field of geometric deep learning (Bronstein et al. 2017; Bronstein et al. 2021).

Geometric deep learning techniques constructed natively on the sphere are essential for next-generation global weather prediction models. McEwen and collaborators have recently developed efficient generalised spherical convolutional neutral networks (Cobb et al. 2021) and spherical scattering networks (McEwen et al. 2022) that have shown exceptional performance. In a recent work they have developed the DISCO framework that is for the first time scalable to high resolution data (Ocampo et al. 2022) opening up dense prediction tasks like cosmological imaging. The DISCO framework provides a saving in computation of 9 orders of magnitude and a saving in memory of 4 orders of magnitude. Moreover, it provides state-of-the-art accuracy in all benchmark problems considered to date. Furthermore, McEwen and collaborators have been developing generative geometric AI techniques based on differentiable spherical harmonic, wavelet and scattering transforms, with a number of papers to be submitted imminently.

The focus of the current project is two-fold. First, further foundations of geometric deep learning on the sphere will be developed, including new types of spherical deep learning layers and architectures, in order to address the open problems in the field, such as scalability to large datasets and interpretability. Second, geometric deep learning techniques on the sphere will be applied to the analysis of cosmological data of the CMB and of cosmic shear, in particular from Euclid and the Rubin Observatory, in order to better understand the nature of dark matter and dark energy. Furthermore, additional applications beyond cosmology, such as for diffusion MRI in medical imaging, may also be considered. The precise focus between these different areas will depend on the interests and expertise of the student.

The student should have a strong mathematical background and be proficient in coding, particularly in Python. The student will gain extensive expertise during the project in deep learning, going far beyond the straightforward application of existing deep learning techniques, instead focusing on novel foundational deep learning approaches and their application to novel problems in cosmology and beyond. The expertise gained in foundational deep learning will prepare the student well for a future career either in academia or industry. In particular, geometric deep learning is a speciality highly sought after in industry by companies such as Twitter, Facebook, Amazon and many others.

### PhD project: Differentiable probabilistic deep learning with generative denoising diffusion models

This project is offered through UCL’s Department of Computer Science and Advanced Research Computing (ARC) Centre. Further details on how to apply are available here.

Please note you will need to use **Funding Reference ARC-PhD** in your application so that it can be routed correctly.

#### Existing background work

Generative AI models for images, such as denoising diffusion models (e.g. Stable Diffusion), have recently demonstrated remarkable performance (Romback et al. 2022). Such generative models can be adapted to solve scientific inverse problems, such as recovering maps of the dark matter of the Universe. However, current approaches typically recover a single prediction, e.g. recover a single image. For robust scientific studies, however, single estimates are not sufficient and a principled statistical assessment is critical in order to quantify uncertainties. Embedding denoising diffusion models in a principled statistical framework for solving inverse problems remains a topical open problem in the field. A number of approximate solutions have been proposed (e.g. Chung et al 2023), however none as yet guarantee that the correct underlying posterior distribution is targeted. McEwen and collaborators have recently developed the proximal nested sampling framework (Cai et al. 2022) for principled statistical inference for high-dimensional inverse imaging problems with convex likelihoods (initial code available at proxnest). Not only is the correct underlying posterior distribution targeted but the framework also supports computation of the marginal likelihood for principled Bayesian model comparison. Recently, the framework has been extended to support deep learned data-driven priors based on simple denoisers (McEwen et al. 2023), although not denoising diffusion models.

#### Main objectives of the project

In this project we will develop a principled statistical framework to sample the posterior distribution of scientific inverse imaging problems that integrates the generative power of denoising diffusion models. This will be achieved by integrating denoising diffusion models into the proximal nested sampling framework. The resulting framework is expected to result in superior reconstruction performance due to the power of generative diffusion models, targets the correct underlying posterior distribution and also allows for Bayesian model comparison to assess different data-driven priors. The framework will be extended beyond convex likelihoods to handle general non-linear models by leveraging automatic differentiation and gradient-based likelihood constraints. Automatic differentiation will also be exploited to accelerate inference. While the focus will be mostly on methodological and code developments, the methods developed will be demonstrated on a number of inverse imaging problems in a range of fields, including cosmology, e.g. mapping dark matter (although note that no prior familiarity with cosmology is required).#### Details of Software/Data Deliverables

The main deliverable with be an open-source code implementing the framework developed. Development will involve differentiable programming, generative denoising diffusion models, and Markov chain Monte Carlo (MCMC) techniques. A number of articles will be prepared as the research progresses, targeting the main deep learning venues (e.g. ICLR, ICML, NeurIPS).## Masters Students

I am not offering any additional Masters projects at present but when I am they will appear here.

## Internship Students

I am not offering any specific internship projects at present. However, if you are interested in discussing internship possibilities further then please email me, including '[Internship enquiry]' in the subject of your email, and attach a CV. I receive many enquires and so will only reply if your expertise are well matched to my research interests and there is a high chance of a placement.